This invention relates to wavelength-tuning, phase-shifting interferometry.
Interferometric optical techniques are widely used to measure optical thickness, flatness, and other geometric and refractive index properties of precision optical components such as glass substrates used in lithographic photomasks.
For example, to measure the surface profile of a measurement surface, one can use an interferometer to combine a measurement wavefront reflected from the measurement surface with a reference wavefront reflected from a reference surface to form an optical interference pattern. Spatial variations in the intensity profile of the optical interference pattern correspond to phase differences between the combined measurement and reference wavefronts caused by variations in the profile of the measurement surface relative to the reference surface. Phase-shifting interferometry (PSI) can be used to accurately determine the phase differences and the corresponding profile of the measurement surface.
With PSI, the optical interference pattern is recorded for each of multiple phase-shifts between the reference and measurement wavefronts to produce a series of optical interference patterns that typically span a full cycle of optical interference (e.g., from constructive, to destructive, and back to constructive interference). The optical interference patterns define a series of intensity values for each spatial location of the pattern, wherein each series of intensity values has a sinusoidal dependence on the phase-shifts with a phase-offset equal to the phase difference between the combined measurement and reference wavefronts for that spatial location. Using numerical techniques known in the art, the phase-offset for each spatial location is extracted from the sinusoidal dependence of the intensity values to provide a profile of the measurement surface relative the reference surface. Such numerical techniques are generally referred to as phase-shifting algorithms.
The phase-shifts in PSI can be produced by changing the optical path length from the measurement surface to the interferometer relative to the optical path length from the reference surface to the interferometer. For example, the reference surface can be moved relative to the measurement surface. Alternatively, the phase-shifts can be introduced for a non-zero optical path difference by changing the wavelength of the measurement and reference wavefronts. The latter application is known as wavelength tuning PSI and is described, e.g., in U.S. Pat. No. 4,594,003 to G. E. Sommargren.
Typically, high-stability light sources are desirable in wavelength-tuning PSI applications as instabilities in the light source (e.g., the mode characteristics) can corrupt PSI data. Mode instabilities, or mode-hops as they are commonly known, cause an unknown and random jump in the phase and frequency of the light source. Accordingly, it is not usually possible to extract an accurate phase from corrupted data.
Because PSI measurements are often required to be extremely accurate and repeatable, highly-stable laser light sources are typically used to prevent mode-hops from occurring, or to stabilize the light before it enters the interferometer. Laser diodes are an inexpensive coherent light source whose wavelength can be tuned by e.g., varying the diode current. Unfortunately, laser diodes often exhibit unpredictable long-term operating mode characteristics. The short cavity of the laser diode, its sensitivity to vibration, optical feedback and temperature, and the unpredictability of aging effects can make the mode characteristics of the laser diode difficult to control. Externally stabilizing the output of a laser diode by coupling the laser diode with an external cavity, or carefully controlling the laser diode environment and fixing the operating mode at a well-defined position can sufficiently improve laser diode stability for use in e.g., PSI applications.
Quasi-stable light sources, such as bare laser diodes, are often overlooked for high-stability applications, like phase-shifting interferometry (PSI). However, the inventors have devised approaches for using a bare laser diode, or other quasi-stable light source, as a source in PSI. Accordingly, the invention is directed to PSI apparatus and methods that utilize non-stabilized light sources, e.g., light sources having mode-instabilities. The inventors have recognized that certain wavelength tunable light sources can be used as a light source for wavelength-tuned interferometers, despite their modal stability. Notably, the inventors have devised PSI implementations wherein laser diodes can be used for interferometric measurements, without the use of additional mode-stabilizing apparatus. In particular, PSI data is acquired regardless of the modal stability of the light. An algorithm, implemented during or after data acquisition, identifies data corrupted by mode instabilities, and eliminates the data from further analysis. Accordingly, the algorithm outputs analyzed data that is free from corruption associated with mode-hops and the like. Moreover, identifying a phase shifting range over which corrupted data sets are collected allows future data to be acquired using a different phase shifting range, potentially avoiding mode instabilities altogether.
In implementations described below, the user accepts that mode hops will occur, rather than trying to fix the operating mode over the use lifetime of the light source. If a controller detects a mod-hop, the controller either changes the light source environment to move the mode-hop out of the wavelength tuning range, or the controller determines the position where the mode-hop occurred and avoids that position during phase processing. These implementations make two assumptions: (i) the range between adjacent mode-hops is larger than the tuning range required by the PSI algorithm for determining a phase; (ii) the light source environment can be changed in sufficiently small increments to move the mode-hop out of the light source tuning range, without moving another mode-hop into the tuning range.
In general, in one aspect, the invention features an interferometry method. The interferometry method includes positioning a measurement surface within an interferometer that derives measurement and reference wavefronts from a tunable coherent light source that exhibits mode-instabilities within a range of wavelengths. The interferometry method further includes measuring an interference signal at each of multiple positions of a series of optical interference patterns produced by the interferometer. Each pattern in the series corresponds to one of multiple wavelengths in the wavelength range of the source. The interferometry method also includes identifying whether a portion of the interference signals is corrupted by a mode-instability in the light source.
Implementations of the interferometry method can include one or more of the following features.
Identifying corrupted portions of the interference signals can include extracting multiple phase values corresponding to different portions of each of at least two of the interference signals. The method can include determining a surface profile corresponding to the different portions. Furthermore, the interferometry can include comparing surface profiles and identifying a corrupt portion based on the comparison. Comparing the surface profiles can include determining a parameter related to a difference between a pair of surface profiles, e.g., the average of the difference at the multiple positions. This parameter can be compared to a noise figure. Comparing the surface profiles can further include comparing the difference between the first mentioned pair of surface profiles to the difference between a second pair of surface profiles.
The interferometry method can include determining a final surface profile from non-corrupted portions of the interference signals. The final surface profile can be determined by averaging surface profiles extracted from the non-corrupted portions of the interference signals.
Each portion of an interference signal can include a series of sequentially measured values, each value corresponding to a respective one of the series of optical interference patterns.
The interferometry method can include ramping from a first wavelength to a second wavelength while measuring the interference signal. The method can also include ramping from the second wavelength to the first wavelength while measuring the interference signal. The interference signal can be phase shifted by an amount sufficient to extract a phase from the interference signal between the first wavelength and the second wavelength. In some embodiments, the interference signal can be phase shifted by an amount sufficient to extract three independent phases from the interference signal between the first wavelength and the second wavelength.
The light source can be a laser, e.g., a laser diode.
The interferometer can be a Fizeau interferometer.
The multiple wavelengths in the wavelength range can be spaced from one another to impart an absolute phase shift between consecutive interference patterns sufficient to extract a phase from each interference signal.
The multiple wavelengths in the wavelength range can be spaced from one another to impart substantially equal phase shifts between consecutive interference patterns.
The interferometry method can include adjusting the light source environment (e.g., the light source temperature) and repeating the measuring and identifying when all when all portions of the interference signal are corrupted.
In another aspect, the invention features an interferometric system, including an interferometer having a mount to position a measurement object relative a reference surface and configured to receive light from a tunable light source and generate an optical interference pattern. The interference pattern includes a superposition of a measurement wavefront of a measurement beam reflected from a surface of the measurement object and a reference wavefront of a reference beam reflected from the reference surface. The interferometric system also includes a detector configured to record an interference signal at multiple locations of the optical interference pattern generated by the interferometer, and a system controller connected to the light source and the detector. During operation, the controller causes the light source to generate light at each of multiple wavelengths, causes the detector to record the interference signals for each of the multiple wavelengths, and implements an algorithm to identify whether a portion of the interference signals is corrupted by a mode-instability in the light source.
Embodiments of the interferometric system can be configured to implement any of the methods, or have any of the features, corresponding to those described with reference to the aforementioned aspect of the invention.
Embodiments of the invention can include one or more of the following advantages. Embodiments of the invention can enable the use of bare single-mode laser diodes in phase-shifting interferometry applications. The overall economy of manufacture of interferometric devices can be improved by using inexpensive light sources, with little or no additional hardware. The wavelength of a light source used in wavelength-tuning PSI can be tuned via current tuning. Interferometric systems can acquire useful data in the presence of mode-instabilities in their light source. Moreover, in some embodiments, if only one mode-hop occurs during any data acquisition, a measurement is produced every time a user initiates a measurement sequence. Interferometric systems can detect when mode instabilities occur, and can automatically correct for their occurrence. Furthermore, interferometric systems can reduce random errors during surface profiling due to averaging.
Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. All publications, patent applications, patents, and other references mentioned herein are incorporated by reference in their entirety. In case of conflict, the present specification, including definitions, will control. In addition, the apparatus, methods, and examples are illustrative only and not intended to be limiting.
Additional features, objects, and advantages of the invention will be apparent from the following detailed description and drawings, and from the claims.